How do you find the mean, median, and mode of the following frequency distribution table?

Score* (Number of Students)
10 - 6
9 - 13
8 - 12
7 - 11
6 - 13
5 - 5

1 Answer
maganbhai P.
Aug 6, 2018

#"Mean "bar(X)=67.55 ," Median " M=8 and "Mode "Z=13#

Explanation:

Let us ordering the data from least to greatest.

Please see the table given below.

Let ,

#x_i="Score" and f_i="Number of students"#

#N="Total Number of students" #

#and Cf_i="Comulative frequency"#

enter image source here

#color(red)((1)"Mean " bar(X)=(sum f_ix_i)/N =(453)/60=67.55#

#"Median " M=((N+1)/2)th " score"to x_i#

#"Median " M=((60+1)/2)th " score"tox_i#

#"Median " M=((30.5)th " score"tox_i#

Now ,from #Cf_ito29 < 30.5 , and 30.5 > 41#

So, see the cell in the green color :

#color(green)(Cf_i=41to "for "x_i=8 #

#:."Median " M=8#

#(3)" Mode " Z="Frequency repeated in the set of data,"#
#color(white)((3)" Mode " Z=)"maximum number of times"#

#:.color(orange)(" Mode " Z=13to"see the yellow color in table for "f_i.#

#i.e." Mode " Z=13#

Hence ,

#"Mean "bar(X)=67.55 ," Median " M=8 and "Mode "Z=13#

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